Chapter 6:Applying the PSSH

Cognitive Science José Luis Bermúdez / Cambridge University Press 2010

Overview

• Explain why ID3 and SHAKEY both count as illustrations of the heuristic search hypothesis

• Introduce frame problem

• Introduce background to the language of thought hypothesis (as an application of the PSSH)

Cognitive Science José Luis Bermúdez / Cambridge University Press 2010

ID3 and PSSH

• ID3 transforms one highly complex symbol structure (database) into another (a decision tree)

• The decision tree itself works by transforming symbol structures according to rules

• Rules are the IF. . . THEN . . . rules built into the decision tree

Cognitive Science José Luis Bermúdez / Cambridge University Press 2010

Heuristic search

• Problems are solved by generating and modifying symbol structures until a solution structure is reached

• Problem-spaces are generally too large to be searched exhaustively (brute force algorithms)

• Search must be selective heuristic search rules

Cognitive Science José Luis Bermúdez / Cambridge University Press 2010

ID3 as heuristic search

• ID3 is a tool for navigating through the search space of decision trees

• The algorithm that it uses sorts through possible decision trees using measures of information gain and entropy reduction

Cognitive Science José Luis Bermúdez / Cambridge University Press 2010

Basic concepts

Entropy – level of uncertainty (relative to a target attribute)

Information gain – reduction of entropy (relative to the target attribute)

The algorithm compares different classifying attributes in order to determine which has the highest information gain

Cognitive Science José Luis Bermúdez / Cambridge University Press 2010

SHAKEY and logic programming

Basic ideas

(1) states in state-spaces characterized by sets of predicate calculus formulas

(2) problems are conjectures to be proved

(3) problem-solving is finding proofs using proof-theoretic techniques and heuristic search techniques

Cognitive Science José Luis Bermúdez / Cambridge University Press 2010

Turn on the light switch

1. Goal wff =

STATUS (SWITCH1, ON)

2. STRIPS solution =

{goto2 (BOX1), climbonbox (BOX 1),

Climboffbox (BOX 1)

Pushto (BOX 1, SWITCH 1)

Climbonbox (BOX 1)

Turnonlight (SWITCH 1)

GO SHAKEY!

Cognitive Science José Luis Bermúdez / Cambridge University Press 2010

The frame problem

• Applying an operator to a state in a state-space problem will affect some relations between objects in the state but not others

• How is the system to keep track of which relations have changed and which not?

• Proofs would be very complicated if there were axioms for each operator specifying the relevant changes and non-changes

Cognitive Science José Luis Bermúdez / Cambridge University Press 2010

Possible framing axiom:

(on C B) & (put B table) (on C B)

Framing axiom?

Cognitive Science José Luis Bermúdez / Cambridge University Press 2010

SHAKEY and the frame problem

SHAKEY has a limited solution to the frame problem built into it

The F-rules in STRIPS have three components• Precondition formula• Delete list• Add formula

The Delete list makes explicit how the state description needs to be altered

Cognitive Science José Luis Bermúdez / Cambridge University Press 2010

Example

• Pickup (x)

• Precondition formula: ONTABLE (x) & HANDEMPTY & CLEAR (x)

• Delete list:{ONTABLE (x), HANDEMPTY, CLEAR (x)}

• Add formula:

HOLDING (x)

Cognitive Science José Luis Bermúdez / Cambridge University Press 2010

Limitations of SHAKEY

• SHAKEY’s explicit solution to the frame problem works only because the microworld is so restricted

• Each operator will only have a small number of effects on the state• These can be explicitly listed

• But this won’t scale up, when we introduce other agents and a more complex environment